I was taught a quick method to straighten grain. Simply pull on the bias of the fabric from one corner to the other. Do it both ways. Then when folding to cut you can see the "drape" if it was not cut straight. Then, with selvedges matched I move one cut end over until the fabric hangs straight when folded. This keeps my cut strips nice and straight with no dog legs. I was never taught the pull a thread method but it does sound like it could come in handy on some fabrics where you really need the straight of grain.